Win-Vector Blog

It occurred to us recently that we don’t have any articles about Bayesian approaches to statistics here. I’m not going to get into the “Bayesian versus Frequentist” war; in my opinion, which style of approach to use is less about philosophy, and more about figuring out the best way to answer a question. Once you have the right question, then the right approach will naturally suggest itself to you. It could be a frequentist approach, it could be a bayesian one, it could be both — even while solving the same problem.

Let’s take the example that Bayesians love to hate: significance testing, especially in clinical trial style experiments. Clinical trial experiments are designed to answer questions of the form “Does treatment X have a discernible effect on condition Y, on average?” To be specific, let’s use the question “Does drugX reduce hypertension, on average?” Assuming that your experiment does show a positive effect, the statistical significance tests that you run should check for the sorts of problems that John discussed in our previous article, Worry about correctness and repeatability, not p-values: What are the chances that an ineffective drug could produce the results that I saw? How likely is it that another researcher could replicate my results with the same size trial?

We can argue about whether or not the question we are answering is the correct question — but given that it is the question, the procedure to answer it and to verify the statistical validity of the results is perfectly appropriate.

So what is the correct question? From your family doctor’s viewpoint, a clinical trial answers the question “If I prescribe drugX to all my hypertensive patients, will their blood pressure improve, on average?” That isn’t the question (hopefully) that your doctor actually asks, though possibly your insurance company does. Your doctor should be asking “If I prescribe drugX to this patient, the one sitting in my examination room, will the patient’s blood pressure improve?” There is only one patient, so there is no such thing as “on average.”

If your doctor has a masters degree in statistics, the question might be phrased as “If I prescribe drugX to this patient, what is the posterior probability that the patient’s blood pressure will improve?” And that’s a bayesian question. Read more…

Related posts:

1. Statistics to English Translation, Part 2a: ’Significant’ Doesn’t Always Mean ’Important’
2. Worry about correctness and repeatability, not p-values
3. Statistics to English Translation, Part 2b: Calculating Significance
4. “I don’t think that means what you think it means;” Statistics to English Translation, Part 1: Accuracy Measures
5. How to test XCOM “dice rolls” for fairness

I was flipping through my copy of William Cleveland’s The Elements of Graphing Data the other day; it’s a book worth revisiting. I’ve always liked Cleveland’s approach to visualization as statistical analysis. His quest to ground visualization principles in the context of human visual cognition (he called it “graphical perception”) generated useful advice for designing effective graphics [1].

I confess I don’t always follow his advice. Sometimes it’s because I don’t agree with him, but also it’s because I use ggplot for visualization, and I’m lazy. I like ggplot because it excels at layering multiple graphics into a single plot and because it looks good; but deviating from the default presentation is often a bit of work. How much am I losing out on by this? I decided to do the work and find out.

Details of specific plots aside, the key points of Cleveland’s philosophy are:

• A graphic should display as much information as it can, with the lowest possible cognitive strain to the viewer.
• Visualization is an iterative process. Graph the data, learn what you can, and then regraph the data to answer the questions that arise from your previous graphic.

Of course, when you are your own viewer, part of the cognitive strain in visualization comes from difficulty generating the desired graphic. So we’ll start by making the easiest possible ggplot graph, and working our way from there — Cleveland style.

Read more…

Related posts:

1. Good Graphs: Graphical Perception and Data Visualization
2. Your Data is Never the Right Shape
3. My Favorite Graphs
4. The cranky guide to trying R packages
5. Please stop using Excel-like formats to exchange data

It’s often the case that I want to write an R script that loops over multiple datasets, or different subsets of a large dataset, running the same procedure over them: generating plots, or fitting a model, perhaps. I set the script running and turn to another task, only to come back later and find the loop has crashed partway through, on an unanticipated error. Here’s a toy example:

> inputs = list(1, 2, 4, -5, 'oops', 0, 10)

> for(input in inputs) {
+   print(paste("log of", input, "=", log(input)))
+ }

[1] "log of 1 = 0"
[1] "log of 2 = 0.693147180559945"
[1] "log of 4 = 1.38629436111989"
[1] "log of -5 = NaN"
Error in log(input) : Non-numeric argument to mathematical function
In addition: Warning message:
In log(input) : NaNs produced

The loop handled the negative arguments more or less gracefully (depending on how you feel about NaN), but crashed on the non-numeric argument, and didn’t finish the list of inputs.

How are we going to handle this?

Read more…

Related posts:

1. R annoyances
2. Your Data is Never the Right Shape
3. Survive R
4. R examine objects tutorial
5. Selection in R

When people ask me what it means to be a data scientist, I used to answer, “it means you don’t have to hold my hand.” By which I meant that as a data scientist (a consulting data scientist), I can handle the data collection, the data cleaning and wrangling, the analysis, and the final presentation of results (both technical and for the business audience) with a minimal amount of assistance from my clients or their people. Not no assistance, of course, but little enough that I’m not interfering too much with their day-to-day job.

This used to be a key selling point, because people with all the necessary skills used to be relatively rare. This is less true now; data science is a hot new career track. Training courses and academic tracks are popping up all over the place. So there is the question: what should such courses teach? Or more to the heart of the question — what does a data scientist do, and what do they need to know?

Read more…

Related posts:

1. Data Science, Machine Learning, and Statistics: what is in a name?
2. Data science project planning
3. Setting expectations in data science projects
4. Your Data is Never the Right Shape
5. Book Review: Ensemble Methods in Data Mining (Seni & Elder)

This was originally posted at ninazumel.com. I’m re-blogging it here.

Photo: John Mount

I came across a post from Emily Willingham the other day: “Is a PhD required for Good Science Writing?”. As a science writer with a science PhD, her answer is: is it not required, and it can often be an impediment. I saw a similar sentiment echoed once by Lee Gutkind, the founder and editor of the journal Creative Nonfiction. I don’t remember exactly what he wrote, but it was something to the effect that scientists are exactly the wrong people to produce literary, accessible writing about matters scientific.

I don’t agree with Gutkind’s point, but I can see where it comes from. Academic writing has a reputation for being deliberately obscure and prolix, jargonistic. Very few people read journal papers for fun (well, except me, but I’m weird). On the other hand, a science writer with a PhD has been trained for critical thinking, and should have a nose for bullpucky, even outside their field of expertise. This can come in handy when writing about medical research or controversial new scientific findings. Any scientist — any person — is going to hype up their work. It’s the writer’s job to see through that hype.

I’m not a science writer in the sense that Dr. Willingham is. I write statistics and data science articles (blog posts) for non-statisticians. Generally, the audience that I write for is professionally interested in the topic, but aren’t necessarily experts at it. And as a writer, many of my concerns are the same as those of a popular science writer.

I want to cut through the bullpucky. I want you, the reader, to come away understanding something you thought you didn’t — or even couldn’t — understand. I want you, the analyst or data science practitioner, to understand your tools well enough to innovate, not just use them blindly. And if I’m writing about one of my innovations, I want you to understand it well enough to possibly use it, not just be awed at my supposed brilliance.

I don’t do these things perfectly; but in the process of trying, and of reading other writers with similar objectives, I’ve figured out a few things.

Read more…

Related posts:

1. What does a generalized linear model do?
2. Kernel Methods and Support Vector Machines de-Mystified
3. Public Service Article: JSTOR and other Useful Research Archives
4. A Personal Perspective on Machine Learning

One of the shortcomings of regression (both linear and logistic) is that it doesn’t handle categorical variables with a very large number of possible values (for example, postal codes). You can get around this, of course, by going to another modeling technique, such as Naive Bayes; however, you lose some of the advantages of regression — namely, the model’s explicit estimates of variables’ explanatory value, and explicit insight into and control of variable to variable dependence.

Here we discuss one modeling trick that allows us to keep categorical variables with a large number of values, and at the same time retain much of logistic regression’s power.

Read more…

Related posts:

1. Modeling Trick: Masked Variables
2. A bit more on impact coding
3. Modeling Trick: the Signed Pseudo Logarithm
4. How robust is logistic regression?
5. Newton-Raphson can compute an average

The important criterion for a graph is not simply how fast we can see a result; rather it is whether through the use of the graph we can see something that would have been harder to see otherwise or that could not have been seen at all.

– William Cleveland, The Elements of Graphing Data, Chapter 2

In this article, I will discuss some graphs that I find extremely useful in my day-to-day work as a data scientist. While all of them are helpful (to me) for statistical visualization during the analysis process, not all of them will necessarily be useful for presentation of final results, especially to non-technical audiences.

I tend to follow Cleveland’s philosophy, quoted above; these graphs show me — and hopefully you — aspects of data and models that I might not otherwise see. Some of them, however, are non-standard, and tend to require explanation. My purpose here is to share with our readers some ideas for graphical analysis that are either useful to you directly, or will give you some ideas of your own.

Read more…

Related posts:

1. The cranky guide to trying R packages
2. Good Graphs: Graphical Perception and Data Visualization
3. Learn Logistic Regression (and beyond)
4. What does a generalized linear model do?
5. Your Data is Never the Right Shape

What is R²? In the context of predictive models (usually linear regression), where y is the true outcome, and f is the model’s prediction, the definition that I see most often is:

In words, R² is a measure of how much of the variance in y is explained by the model, f.

Under “general conditions”, as Wikipedia says, R² is also the square of the correlation (correlation written as a “p” or “rho”) between the actual and predicted outcomes:

I prefer the “squared correlation” definition, as it gets more directly at what is usually my primary concern: prediction. If R² is close to one, then the model’s predictions mirror true outcome, tightly. If R² is low, then either the model does not mirror true outcome, or it only mirrors it loosely: a “cloud” that — hopefully — is oriented in the right direction. Of course, looking at the graph always helps:

The question we will address here is : how do you get from R² to correlation?

Read more…

Related posts:

1. What does a generalized linear model do?
2. The Simpler Derivation of Logistic Regression
3. The equivalence of logistic regression and maximum entropy models
4. Level fit summaries can be tricky in R
5. Statistics to English Translation, Part 2b: Calculating Significance

Logistic regression is one of the most popular ways to fit models for categorical data, especially for binary response data. It is the most important (and probably most used) member of a class of models called generalized linear models. Unlike linear regression, logistic regression can directly predict probabilities (values that are restricted to the (0,1) interval); furthermore, those probabilities are well-calibrated when compared to the probabilities predicted by some other classifiers, such as Naive Bayes. Logistic regression preserves the marginal probabilities of the training data. The coefficients of the model also provide some hint of the relative importance of each input variable.

While you don’t have to know how to derive logistic regression or how to implement it in order to use it, the details of its derivation give important insights into interpreting and troubleshooting the resulting models. Unfortunately, most derivations (like the ones in [Agresti, 1990] or [Hastie, et.al, 2009]) are too terse for easy comprehension. Here, we give a derivation that is less terse (and less general than Agresti’s), and we’ll take the time to point out some details and useful facts that sometimes get lost in the discussion. Read more…

Related posts:

1. The equivalence of logistic regression and maximum entropy models
2. How robust is logistic regression?
3. Learn Logistic Regression (and beyond)
4. Large Data Logistic Regression (with example Hadoop code)
5. What does a generalized linear model do?

Research surveys tend to fall on either end of the spectrum: either they are so high level and cursory in their treatment that they are useful only as a dictionary of terms in the field, or they are so deep and terse that the discussion can only be followed by those already experienced in the field. Ensemble Methods in Data Mining (Seni and Elder, 2010) strikes a good balance between these extremes. This book is an accessible introduction to the theory and practice of ensemble methods in machine learning, with sufficient detail for a novice to begin experimenting right away, and copious references for researchers interested in further details of algorithms and proofs. The treatment focuses on the use of decision trees as base learners (as they are the most common choice), but the principles discussed are applicable with any modeling algorithm. The authors also provide a nice discussion of cross-validation and of the more common regularization techniques.

The heart of the text is the chapter on the Importance Sampling. The authors frame the classic ensemble methods (bagging, boosting, and random forests) as special cases of the Importance Sampling methodology. This not only clarifies the explanations of each approach, but also provides a principled basis for finding improvements to the original algorithms. They have one of the clearest explanations of AdaBoost that I’ve ever read.

A major shortcoming of ensemble methods is the loss of interpretability, when compared to single-model methods such as Decision Trees or Linear Regression. The penultimate chapter is on “Rule Ensembles”: an attempt at a more interpretable ensemble learner. They also discuss measures for variable importance and interaction strength. The last chapter discusses Generalized Degrees of Freedom as an alternative complexity measure and its relationship to potential over-fit.

Overall, I found the book clear and concise, with good attention to practical details. I appreciated the snippets of R code and the references to relevant R packages. One minor nitpick: this book has also been published digitally, presumably with color figures. Because the print version is grayscale, some of the color-coded graphs are now illegible. Usually the major points of the figure are clear from the context in the text; still, the color to grayscale conversion is something for future authors in this series to keep in mind.

Recommended.

Related posts:

1. A Demonstration of Data Mining
2. SIGACT Review of: Combinatorics the Rota Way
3. Kernel Methods and Support Vector Machines de-Mystified
4. Good Graphs: Graphical Perception and Data Visualization
5. Setting expectations in data science projects